1. Field of the Invention
The present invention relates to the field of characterization of fractured porous media, that is media where the presence of fractures plays an important part in the physical properties of the medium. In particular, the invention relates to a method of constructing a fracture density log (FIG. 2) of a porous formation traversed by a series of fractures and at least one borehole.
2. Description of the Prior Art
Fractures contribute to reducing the resistance capacities of the rock and they can significantly increase the ease of circulation of the fluid (mean permeability) in relation to the properties of the sound rock. In most cases, studying these media requires information on the density of the fractures contained therein. For example, knowledge of the 3D fracture density in a rock is crucial in the field of civil engineering in order to predict the behavior of the rock during the construction of a piece of work such as a tunnel. This density is also fundamental for estimating the mean hydrodynamic properties of rocks affected by a fracture network. As a complement to the orientation and length distribution, the fracture density directly influences the fracture connectivity. In the case of petroleum exploration and production, the fracture density defines the size of the sound matrix blocks containing the oil in place, and it controls the connection between these blocks and a producer well (or an injector well in the case of enhanced recovery or CO2 sequestration). Knowledge of the fracture network is also important information in the field of hydrogeology for aquifer characterization.
The understanding and even the prediction of flows in fractured reservoirs is the subject of numerical models at the reservoir scale or in the vicinity of the wells. In order to perform simulations by means of softwares referred to as flow simulators, it is necessary to construct:                a structural model with the geometries of the rock layers and of the large faults that carve them;        a lithologic model generally constructed by means of geostatistical tools or from numerical sediment transport simulations, by assigning to each lithology properties relative to the flows;        in the case of fractured reservoirs, a model of the distribution and of the properties of the fractures within an elementary volume representative of the reservoir.        
The statistical properties of the fractures and the flow properties of a homogeneous elementary volume equivalent to the fractured rocks volume are the input parameters of the flow models in reservoirs.
Characterization of the fractures in terms of orientation, density and hydrodynamic properties is essential for modelling flows in reservoirs. Reservoir formations cover several tens of kilometers laterally and are located at depths of the order of one hundred meters for aquifers, and generally several kilometers for hydrocarbon reservoirs. The only fracture observation data available come from the wells (coring or imaging). More precisely, these data relate to the intersection of the fractures with the well walls and they therefore only allow sparse reservoir sampling.
In order to estimate the density, a first approach counts the number of fractures per well length unit, denoted by density P10. According to a known measurement bias, there is little chance that the fractures that are more or less parallel to the wells will intercept it in comparison with those that are greatly oblique thereto. This bias is then corrected by weighting each fracture intersection by a function that decreases with the obliquity of the fractures in relation to the well (“Terzaghi R. D., Sources of Error in Joint Surveys. Géotechnique, 15: 287-304”). One major drawback of this method is that it does not take into account the influence of the length distribution on the correction factor, which plays an important part when the size of the fractures is comparable to or smaller than the radius of the well, and their intersection with the well wall is frequently expressed by partial traces (fracture that does not completely intersect the cross section of the well) (“Mauldon, M. and Mauldon, J. G. Fracture Sampling on a Cylinder. From Scanlines to Boreholes and Tunnels. Rock Mech. Rock Engng. 30(3): 129-144, 1997”).
A second approach estimates the three-dimensional density, denoted by density P32, within a well core interval, while considering it to be representative of density P32 in a reservoir volume. In an equivalent manner (“Narr W. Estimating Average Fracture Spacing in Subsurface Rock, AAPG Bulletin, 90, 10: 1565-1586, 1996”), by proposing constant opening of the fractures, a ratio is calculated between the volume of a core interval and the sum of the volumes within the fractures, and this ratio is assumed to be equal to its measurement in a reservoir volume.
A third method consists in:
1—generating discrete fracture network models by varying density P32 for given orientation and length laws;
2—calculating the intersection of these models with the well interval so as to obtain the corresponding densities P10; and
3—seeking, from the cluster of points (P10,P32) obtained, the linear regression curve that best satisfies (in the sense of the least squares) the relation between P32 and P10.
This linear relation is then used to provide a value for P32 for each observation of P10. This method, unlike the previous ones, is akin to a Monte-Carlo method and it involves the drawback of a long calculating time. However, by using networks generated by means of statistical laws provided by the user, it takes implicitly into account the biases due to the orientation and length distributions. It has notably been applied (in “Starzec P. and C-F Tsang. Use of Fracture-Intersection Density for Predicting the Volume of Unstable Blocks in Underground Openings”, International Journal of Rock Mechanics & Mining Sciences, 39: 807-813, 2002″) to establish on the one hand a relation between density P32 and density P10 and, on the other hand, a relation between density P32 and the number of fractures that have an intersection with a plane surface.
Because of the sparse reservoir sampling by the measurement intervals on the well, the uncertainty on the possible value of P32 knowing P10 can be large (see FIG. 5). Now, the three methodologies presented above only provide an estimation of a mean density P32 for each observation of P10 and they do not give the uncertainty associated with this value.
The invention relates to an alternative method of constructing a fracture density log of a porous formation, from observations of the intersections of fracture traces on the walls of a borehole traversing the medium. The method overcomes the difficulties of the prior art by estimating, by means of an analytical formula, a conditional probability law of the three-dimensional fracture density, knowing the number of intersections.